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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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1435-5337
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Volume 29, Issue 3

Issues

Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups

Constantin-Cosmin Todea
  • Corresponding author
  • Department of Mathematics, Technical University of Cluj-Napoca, Str. G. Baritiu 25, Cluj-Napoca 400027, Romania
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Published Online: 2016-07-21 | DOI: https://doi.org/10.1515/forum-2015-0185

Abstract

We give an explicit approach for Bockstein homomorphisms of the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use an additive decomposition and a product formula for the Hochschild cohomology of group algebras given by Siegel and Witherspoon in 1999. For an algebraically closed field k of characteristic p and a finite group G we prove an additive decomposition and a product formula for the cohomology algebra of a defect group of a block ideal of kG with coefficients in the source algebra of this block, and we define similar Bockstein homomorphisms.

Keywords: Finite; group; block; Hochschild; cohomology; Bockstein

MSC 2010: 16Exx; 20C20

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About the article


Received: 2015-09-17

Revised: 2016-05-17

Published Online: 2016-07-21

Published in Print: 2017-05-01


Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 735–749, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0185.

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